1answer.
Ask question
Login Signup
Ask question
All categories
  • English
  • Mathematics
  • Social Studies
  • Business
  • History
  • Health
  • Geography
  • Biology
  • Physics
  • Chemistry
  • Computers and Technology
  • Arts
  • World Languages
  • Spanish
  • French
  • German
  • Advanced Placement (AP)
  • SAT
  • Medicine
  • Law
  • Engineering
kompoz [17]
3 years ago
15

Given an arithmetic sequence with a3=5 and a5=19, find the 24th term.

Mathematics
1 answer:
krok68 [10]3 years ago
5 0

The 24th term is 152

Step-by-step explanation:

The formula of the nth term of an arithmetic sequence is:

a_n=a+(n-1)d , where

  • a is the first term
  • d is the common difference between consecutive terms

The third term means n = 3

∵ a_3=a+(3-1)d

∴ a_3=a+2d

∵ a_3 = 5

- Equate the right hand sides of the third term

∴ a + 2d = 5 ⇒ (1)

The fifth term means n = 5

∵ a_5=a+(5-1)d

∴ a_5=a+4d

∵ a_5 = 19

- Equate the right hand sides of the fifth term

∴ a + 4d = 19 ⇒ (2)

Now we have a system of equations to solve it

Subtract equation (1) from equation (2) to eliminate a

∴ 2d = 14

- Divide both sides by 2

∴ d = 7

- Substitute the value of d in equation (1) to find a

∵ a + 2(7) = 5

∴ a + 14 = 5

- Subtract 14 from both sides

∴ a = -9

The twenty fourth term means n = 24

∵ a = -9 and d = 7

- Substitute the values of a and d in the formula of the nth term

∴ a_24=-9+(24-1)(7)

∴ a_24=-9+(23)(7)

∴ a_24=-9+161

∴ a_24=152

The 24th term is 152

Learn more:

You can learn more about the arithmetic sequence in brainly.com/question/7221312

#LearnwithBrainly

You might be interested in
Use pictures or words to explain how to use the sum of 13 to show how to add in any order
schepotkina [342]
3+3+4+3 im sure this is the answer just double chek



6 0
3 years ago
If a is a negative number, then a(1/a) is equal to -1. If a is a negative number and b is a negative number, then product ab is
Firdavs [7]

Both claims are false. In fact, a and \frac{1}{a} are one the multiplicative inverse of the other. This means, by definition of multiplicative inverse, that

a \cdot \dfrac{1}{a} = 1 \quad\forall a \in \mathbb{R}

So, it doesn't matter if a is positive or negative: the multiplication of one number and its inverse will always be 1: for example,

(-2) \cdot \dfrac{1}{-2} = \dfrac{-2}{-2} = 1

Similarly, when you multiply two number, the sign of the product depends on the sign of the factors as follows:

  • (+) \cdot (+) = (+)
  • (+) \cdot (-) = (-)
  • (-) \cdot (+) = (-)
  • (-) \cdot (-) = (+)

So, the multiplication of two negative numbers is a positive number.

8 0
3 years ago
Dan bought a new computer for $900. Each year, the value of the computer decreased by 25% of the previous year’s value.
Anna35 [415]

Answer:

$29, that is the answer for this question

8 0
3 years ago
It is generally claimed that the average body temperature for healthy human adults is 98.6°F. To test this claim a simple random
Rzqust [24]

Answer:

Explained below.

Step-by-step explanation:

The information provided is as follows:

\mu=98.6^{o}F\\\bar x=98.1^{o}F\\s=0.9^{o}F\\n=9

(1)

A single mean test is to be performed in this case.

As the population standard deviation is not provided, a one-sample <em>t</em>-test will be used.

The correct option is b.

(2)

The null hypothesis is:

<em>H</em>₀: The average temperature in the population is 98.6°F, i.e. <em>μ </em>= 98.6°F.

The correct option is b.

(3)

The alternative hypothesis is:

<em>Hₐ</em>: The average temperature in the population is less than 98.6°F, i.e. <em>μ </em>< 98.6°F.

The correct option is c.

(4)

The standard deviation of the sample mean is as follows:

SD_{\bar x}=\frac{s}{\sqrt{n}}=\frac{0.9}{\sqrt{9}}=0.3^{o}F

Thus, the value of SD is 0.3°F.

(5)

Compute the value of test statistic as follows:

t=\frac{\bar x-\mu}{SD_{\bar x}}

  =\frac{98.1-98.6}{0.3}\\\\=-1.666666667\\\\\approx -1.67

Thus, the value of test statistic is -1.67.

(6)

The degrees of freedom of the test are:

df = n - 1

   = 9 - 1

   = 8

Thus, the degrees of freedom of the test is 8.

8 0
3 years ago
Solve for r in the scientific formula d = rt.<br><br> r = _______
marta [7]
R = d/t is the answer. Hope this helped
4 0
2 years ago
Read 2 more answers
Other questions:
  • Please help!!!!
    12·1 answer
  • Someone help me!! Pls
    8·1 answer
  • Punkt p (1;2k+1) należy do wykresu funkcji f(x)=-4x2+7. Oblicz k
    7·1 answer
  • Which inequality is represented by this graph?
    7·1 answer
  • Numbers:20 &amp; 21 <br> Please help me!!!!
    6·1 answer
  • The price of a television increased from $325 to $390. By what percentage was the price of the television increased?
    11·1 answer
  • Please help if you can !!!
    5·1 answer
  • A movie complex is showing the same movie in three theaters. In theater​ A, 56 of the 80 seats are taken. In theater​ B, seats a
    11·1 answer
  • 6-2x=6x-10x+14 what is the value of x
    11·2 answers
  • A baker has 72 vanilla cupcakes and 80 chocolate cupcakes. She wants to make platters that have both kinds of cupcakes, and she
    9·2 answers
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!